In this paper we analyze general deterministic epidemiological models described by autonomous ordinary differential equations taking into account heterogeneity related to the infectivity and vital dynamics, in which the flow into the compartment of the susceptible individuals is given by a generic function. Our goal is to provide a new tool that facilitates the qualitative analysis of equilibrium points, which represent the disease free population, generalizing the result presented by Leite et al. (Math Med Biol J IMA 17:15–31, 2000) , and population extinction. The epidemiological models exposed are the type SEIRS (Susceptible-Exposed-Infectious-Recovered-Susceptible) and SEIR (Susceptible-Exposed-Infectious-Recovered) with vaccination. Moreover, we computed the basic reproduction number from the models by van den Driessche and Watmough (Math Biosci 180:29–48, 2002) and correlate this threshold parameter with the stability of the equilibrium point representing the disease free population.

中文翻译：

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包含异质传染性的流行病学模型的稳定性分析

在本文中，我们分析了由自主常微分方程描述的一般确定性流行病学模型，其中考虑了与传染性和生命动态有关的异质性，其中流入易感个体的区室由通用函数给出。我们的目标是提供一种新工具，以简化代表无病人群的平衡点的定性分析，从而概括Leite等人的结果。（Math Med Biol J IMA 17：15-31，2000），以及种群灭绝。暴露的流行病学模型是带有疫苗接种的SEIRS型（易感暴露传染恢复型）和SEIR（易感暴露传染恢复型）。此外，